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Setting up a theory of stability of fibrous and laminated composites

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International Applied Mechanics Aims and scope

The results obtained in setting up a theory of stability of fibrous and laminated composites in the case where the plane Π is in an arbitrary position are analyzed. The plane Π is formed by the points of a buckling mode that have equal phases relative to the line of compression. This theory follows from the linearized three-dimensional theory of stability of deformable bodies and is used to determine the critical compressive load and the associated position of the plane Π. Numerical examples are presented. A brief historical sketch is given

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References

  1. A. N. Guz, “On setting up a stability theory of unidirectional fibrous materials,” Int. Appl. Mech., 5, No. 2, 156–162 (1969).

    MathSciNet  Google Scholar 

  2. A. N. Guz, “Determining the theoretical compressive strength of reinforced materials,” Dokl. AN USSR, Ser. A, No. 3, 236–238 (1969).

  3. A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1971).

    Google Scholar 

  4. A. N. Guz, Stability of Elastic Bodies under Finite Deformation [in Russian], Naukova Dumka, Kyiv (1973).

    Google Scholar 

  5. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kyiv (1986).

    Google Scholar 

  6. A. N. Guz, Elastic Waves in Prestressed Bodies [in Russian], Naukova Dumka, Kyiv (1986).

    Google Scholar 

  7. A. N. Guz, Fracture Mechanics of Composites under Compression [in Russian], Naukova Dumka, Kyiv (1990).

    Google Scholar 

  8. A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A.S.K., Kyiv (2004).

    Google Scholar 

  9. A. N. Guz and V T. Golovchan, Diffraction of Elastic Waves in Multiply Connected Bodies [in Russian], Naukova Dumka, Kyiv (1972).

    Google Scholar 

  10. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Plane problems of stability of composite materials with a finite-size filler,” Mech. Comp. Mater., 36, No. 1, 49–54 (2000).

    Article  Google Scholar 

  11. I. Yu. Babich and A. N. Guz, “Stability of composite structural members (three-dimensional formulation),” Int. Appl. Mech., 38, No. 9, 1048–1075 (2002).

    Article  Google Scholar 

  12. I. Yu. Babich, A. N. Guz, and V. N. Chekhov, “The three-dimensional theory of stability of fibrous and laminated materials,” Int. Appl. Mech., 37, No. 9, 1103–1141 (2001).

    Article  Google Scholar 

  13. S. Yu. Babich, A. N. Guz, and V. B. Rudnitskii, “Contact Problems for prestressed elastic bodies and rigid and elastic punches,” Int. Appl. Mech., 40, No. 7, 744–765 (2004).

    Article  Google Scholar 

  14. A. M. Bagno and A. N. Guz, “Elastic waves in prestressed bodies interacting with a fluid (survey),” Int. Appl. Mech., 33, No. 6, 435–463 (1997).

    Article  MathSciNet  Google Scholar 

  15. V. A. Dekret, “Two-dimensional buckling problem for a composite reinforced with a periodic row of a collinear short fibers,” Int. Appl. Mech., 42, No. 6, 684–691 (2006).

    Article  Google Scholar 

  16. A. N. Guz, “On local instability of fiber composites,” Dokl. Akad. Nauk SSSR, 314, No. 4, 806–809 (1990).

    Google Scholar 

  17. A. N. Guz, “Stability theory for unidirectional fiber-reinforced composites,” Int. Appl. Mech., 32, No. 8, 577–586 (1996).

    Article  MATH  Google Scholar 

  18. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer Berlin–Heidelberg–New-York–Tokyo (1999).

    MATH  Google Scholar 

  19. A. N. Guz, “Constructing the three-dimensional theory of stability of deformable bodies,” Int. Appl. Mech., 37, No. 1, 1–37 (2001).

    Article  Google Scholar 

  20. A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23–59 (2002).

    Article  MathSciNet  Google Scholar 

  21. A. N. Guz, “Establishing the fundamentals of the theory of stability of mine workings,” Int. Appl. Mech., 39, No. 1, 20–48 (2003).

    Article  Google Scholar 

  22. A. N. Guz, “On one two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).

    Article  Google Scholar 

  23. A. N. Guz, “Design models in linearized solid mechanics,” Int. Appl. Mech., 40, No. 5, 506–516 (2004).

    Article  MathSciNet  Google Scholar 

  24. A. N. Guz, “Three-dimensional theory of stability of a carbon nanotube in matrix,” Int. Appl. Mech., 42, No. 1, 19–31 (2006).

    Article  MathSciNet  Google Scholar 

  25. A. N. Guz, “On study of nonclassical problems of fracture and failure mechanics and related mechanisms,” Int. Appl. Mech., 45, No. 1, 1–31 (2009).

    Article  Google Scholar 

  26. A. N. Guz, S. Yu. Babich, and V. B. Rudnitskii, “Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research,” Appl. Mech. Rev., 51, No. 5, 343–371 (1998).

    Article  Google Scholar 

  27. A. N. Guz and V. N. Chekhov, “Problems of folding in the Earth’s stratified crust,” Int. Appl. Mech., 43, No. 2, 127–159 (2007).

    Article  Google Scholar 

  28. A. N. Guz and V. A. Dekret, “Interaction of two parallel short fibers in the matrix at loss of stability,” CMES, 13, No. 4, 165–170 (2006).

    Google Scholar 

  29. A. N. Guz and V. A. Dekret, “On two models in the three-dimensional theory of stability of composite materials,” Int. Appl. Mech., 44, No. 8, 839–854 (2008).

    Article  Google Scholar 

  30. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Solution of plane problems of the three-dimensional stability of a ribbon-reinforced composite,” Int. Appl. Mech., 36, No. 10, 1317–1328 (2000).

    Article  Google Scholar 

  31. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Two-dimensional stability problem for two interacting short fibers in composite. In-line arrangement,” Int. Appl. Mech., 40, No. 9, 994–1001 (2004).

    Article  Google Scholar 

  32. A. N. Guz, V. A. Dekret, and Yu. V. Kokhanenko, “Planar stability problem of composite weakly reinforced by short fibers,” Mech. Adv. Mater. Struct., No. 12, 313–317 (2005).

  33. A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: Approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).

    Article  Google Scholar 

  34. A. N. Guz and I. A. Guz, “On the theory of stability of laminated composites,” Int. Appl. Mech., 35, No. 4, 323–329 (1999).

    Article  MathSciNet  Google Scholar 

  35. A. N. Guz and I. A. Guz, “Analytical solution of stability problem for two composite half-planes compressed along cracks,” Composites: Part B, 31, No. 5, 405–418 (2000).

    Article  Google Scholar 

  36. A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 1. Exact solutions for the case of unequal roots,” Int. Appl. Mech., 36, No. 4, 482–491 (2000).

    Article  Google Scholar 

  37. A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 2. Exact solutions for the case of equal roots,” Int. Appl. Mech., 36, No. 5, 615–622 (2000).

    Article  MathSciNet  Google Scholar 

  38. A. N. Guz and I. A. Guz, “The stability of the interface between two bodies compressed along interface cracks. 3. Exact solutions for the combined case of equal and unequal roots,” Int. Appl. Mech., 36, No. 6, 759–768 (2000).

    Article  MathSciNet  Google Scholar 

  39. A. N. Guz and I. A. Guz, “Mixed plane problems in linearized solid mechanics. Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).

    Article  MathSciNet  Google Scholar 

  40. A. N. Guz and I. A. Guz, “On models in the theory of stability of multiwalled carbon nanotubes,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).

    Article  MathSciNet  Google Scholar 

  41. A. N. Guz and Yu. I. Khoma, “Stability of an infinite solid with a circular cylindrical crack under compression using the Treloar potential,” Theor. Appl. Fract. Mech., 39, No. 3, 276–280 (2002).

    Google Scholar 

  42. A. N. Guz and Yu. I. Khoma, “Integral formulation for a circular cylindrical cavity in infinite solid and finite length coaxial cylindrical crack compressed axially,” Theor. Appl. Fract. Mech., 45, No. 3, 204–211 (2006).

    Article  Google Scholar 

  43. A. N. Guz, Yu. I. Khoma, and V. M. Nazarenko, “On fracture of an infinite elastic body in compression along a cylindrical defect,” in: Proc. ICF 9 Advances in Fracture Research, Vol. 4, Sydney, Australia (1997), pp. 2047–2054.

  44. A. N. Guz and Yu. N. Lapusta, “Three-dimensional problems of the near-surface instability of fiber composites in compression (model of a piecewise-uniform medium) (survey),” Int. Appl. Mech., 35, No. 7, 641–670 (1999).

    Article  Google Scholar 

  45. A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “A 3-D periodic instability model for a series of fibers in a matrix,” Adv. Compos. Let., 9, No. 2, 93–100 (2000).

    Google Scholar 

  46. A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “A micromechanics solutions of a 3D internal instability problem for a fiber series in an infinite matrix,” Int. J. Fract., 116, No. 3, L55–L60 (2002).

    Article  Google Scholar 

  47. A. N. Guz, Yu. N. Lapusta, and A. N. Samborskaya, “3D model and estimation of fiber interaction effects during internal instability in non-linear composites,” Int. J. Fract., 134, No. 3–4, L45–L51 (2005).

    Article  Google Scholar 

  48. A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondestructive stress analysis of solids,” Int. Appl. Mech., 36, No. 9, 1119–1149 (2000).

    Article  Google Scholar 

  49. A. N. Guz, V. M. Nazarenko, and Yu. I. Khoma, “Fracture of an infinite incompressible hyperelastic material under compression along a cylindrical crack,” Int. Appl. Mech., 32, No. 5, 325–331 (1996).

    Article  MATH  Google Scholar 

  50. A. N. Guz, A. A. Rodger, and I. A. Guz, “Developing a compressive failure theory of nanocomposites,” Int. Appl. Mech., 41, No. 3, 233–255 (2005).

    Article  Google Scholar 

  51. I. A. Guz, J. J. Rushchitsky, and I. A. Guz, “Establishing fundamentals of the mechanics of nanocomposites,” Int. Appl. Mech., 43, No. 3, 247–271 (2007).

    Article  Google Scholar 

  52. A. N. Guz and A. N. Samborskaya, “General stability problem of a series of fibers in an elastic matrix,” Int. Appl. Mech., 27, No. 3, 223–231 (1991).

    MATH  Google Scholar 

  53. A. N. Guz and A. P. Zhuk, “Motion of solid particles in a liquid under the action of an acoustic field: The mechanism of radiation pressure,” Int. Appl. Mech., 40, No. 3, 246–265 (2004).

    Article  Google Scholar 

  54. I. A. Guz, “Spatial nonsymmetric problems of the theory of stability of laminar highly elastic composite materials,” Int. Appl. Mech., 25, No. 11, 1080–1085 (1989).

    MATH  Google Scholar 

  55. I. A. Guz, “On local instability of laminated composite materials,” Dokl. Akad. Nauk SSSR, 311, No. 4, 812–814 (1990).

    MathSciNet  Google Scholar 

  56. I. A. Guz, “Stability of a composite with two interface microcracks under compression,” Dokl. Akad. Nauk SSSR, 328, No. 4, 437–439 (1993).

    Google Scholar 

  57. I. A. Guz, “Stability of a composite with interlayer cracks under compression,” Dokl. Akad. Nauk SSSR, 325, No. 3, 455–458 (1992).

    Google Scholar 

  58. I. A. Guz and A. N. Guz, “Stability of two different half-planes in compression along interfacial cracks: Analytical solutions,” Int. Appl. Mech., 37, No. 7, 906–912 (2001).

    Article  MathSciNet  Google Scholar 

  59. I. A. Guz, A. A. Rodger, A. N. Guz, abd J. J. Rushchitsky, “Developing the mechanical models for nanomaterials,” Composites: Part A, 38, 1234–1250 (2007).

    Article  Google Scholar 

  60. Ch. Jochum and J.-C. Grandidier, “Microbuckling elastic modeling approach of a single carbon fiber embedded in a epoxy matrix,” Compos. Sci. Techn., 64, 2441–2449 (2004).

    Article  Google Scholar 

  61. “Micromechanics of composite materials: Focus on Ukrainian research,” Appl. Mech. Rev., Special Issue, 45, No. 2, 13–101 (1992).

  62. A. N. Samborskaya, “Stability loss of a series of fibers in an elastic matrix with highly elastic deformation,” Int. Appl. Mech., 27, No. 7, 665–669 (1991).

    Google Scholar 

  63. M. A. Wadee, G. W. Hunt, and M. A. Peletier, “Kink band instability in layered structures,” J. Mech. Phys. Solids, 52, 1071–1091 (2004).

    Article  MATH  ADS  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterov St., Kyiv, Ukraine, 03057

    A. N. Guz

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  1. A. N. Guz
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Correspondence to A. N. Guz.

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Translated from Prikladnaya Mekhanika, Vol. 45, No. 6, pp. 4–41, June 2009.

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Guz, A.N. Setting up a theory of stability of fibrous and laminated composites. Int Appl Mech 45, 587–612 (2009). https://doi.org/10.1007/s10778-009-0216-5

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